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 A203621 Highly anti-imperfect numbers: numbers k that sets a record for the value of |sigma*(k)-k|, where sigma*(k) is the sum of the anti-divisors of k. 1
 1, 2, 7, 10, 13, 17, 22, 27, 28, 32, 38, 45, 52, 60, 63, 67, 77, 95, 105, 130, 137, 143, 157, 158, 175, 193, 203, 247, 297, 315, 357, 423, 462, 472, 473, 578, 675, 682, 742, 770, 787, 1012, 1138, 1215, 1417, 1463, 1732, 1957, 2047, 2048, 2327, 2363, 2632 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Anti-imperfect numbers are anti-deficient numbers or anti-abundant numbers. LINKS Amiram Eldar, Table of n, a(n) for n = 1..600 (terms 1..100 from Paolo P. Lava) EXAMPLE n=1. Anti-divisors: 0. |0-1|=1 n=2. Anti-divisors: 0. |0-2|=2 n=3. Anti-divisors: 2. |2-3|=1 less than 2: 3 is not in the sequence. n=4. Anti-divisors: 3. |3-4|=1 less than 2: 4 is not in the sequence. n=5. Anti-divisors: 2,3. |5-3|=2 equal to the maximum: 5 is not in the sequence. n=6. Anti-divisors: 4. |4-6|=2 equal to the maximum: 6 is not in the sequence. n=7. Anti-divisors: 2,3,5. |10-7|=3 new maximum: 7 is in the sequence. MAPLE P:=proc(i) local a, k, n, s; s:=0; for n from 1 to i do a:=0; for k from 2 to n-1 do if abs((n mod k)- k/2)<1 then a:=a+k; fi; od; if abs(n-a)>s then s:=abs(n-a); print(n); fi; od; end: P(3000); MATHEMATICA sig[n_] := Total[Cases[Range[2, n - 1], _?(Abs[Mod[n, #] - #/2] < 1 &)]]; d[n_] := Abs[sig[n] - n]; s = {}; dm = -1; Do[If[(d1 = d[n]) > dm, dm = d1; AppendTo[s, n]], {n, 1, 2700}]; s (* Amiram Eldar, Jan 13 2022 after Michael De Vlieger at A066417 *) CROSSREFS Cf. A066417, A074918, A192267, A192268. Sequence in context: A277551 A029904 A026364 * A297832 A003158 A130336 Adjacent sequences: A203618 A203619 A203620 * A203622 A203623 A203624 KEYWORD nonn AUTHOR Paolo P. Lava, Jan 04 2012 STATUS approved

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Last modified April 19 02:28 EDT 2024. Contains 371782 sequences. (Running on oeis4.)